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Simplifying 11a + 7d + -7a + -5d + 1 = 0 Reorder the terms: 1 + 11a + -7a + 7d + -5d = 0 Combine like terms: 11a + -7a = 4a 1 + 4a + 7d + -5d = 0 Combine like terms: 7d + -5d = 2d 1 + 4a + 2d = 0 Solving 1 + 4a + 2d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 4a + -1 + 2d = 0 + -1 Reorder the terms: 1 + -1 + 4a + 2d = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4a + 2d = 0 + -1 4a + 2d = 0 + -1 Combine like terms: 0 + -1 = -1 4a + 2d = -1 Add '-2d' to each side of the equation. 4a + 2d + -2d = -1 + -2d Combine like terms: 2d + -2d = 0 4a + 0 = -1 + -2d 4a = -1 + -2d Divide each side by '4'. a = -0.25 + -0.5d Simplifying a = -0.25 + -0.5d
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